The Geometry of the Universe

摘要: One of the most fruitful sources mathematical intuition is physical space. For not only does space provide us with basic concepts Euclidean geometry, but it also gives a pictorial framework for visualizing very much more general types that occur continually throughout mathematics. Moreover, was picture led to those key ideas analysis: continuity and smoothness. Indeed, even notion real number originated from measurement spatial separation—and time intervals too, these being, as Albert Einstein’s relativity has told us, geometrical quantities again, whose essentially bound up So comes shock when we learn our now cherished geometry not, after all, describe in accurate way. Yet, beginnings, subtle flexible known differential grown maturity. It terms this theory finds expression. And now, than sixty years first put forward daring original view world, stands excellent agreement observation. if wish understand how world shaped, must come theory.